Lattice Boltzmann model for the incompressible Navier-Stokes equation

In this paper a lattice Boltzmann (LB) model to simulate incompressible flow is developed. The main idea is to explicitly eliminate the terms of o(M-2), where M is the Mach number, due to the density fluctuation in the existing LB models. In the proposed incompressible LB model, the pressure p instead of the mass density p is the independent dynamic variable. The incompressible Navier-Stokes equations are derived from the incompressible LB model via Chapman-Enskog procedure. Numerical results of simulations of the plane Poiseuille now driven either by pressure gradient or a Fixed velocity profile at entrance as well as of the 2D Womersley flow are presented. The numerical results are found to be in excellent agreement with theory.